Modelling functionally graded materials in heat transfer and thermal stress analysis by means of graded finite elements

Abstract

For better understanding of the behavior of functionally graded materials (FGM) in high temperature environment, a reliable and efficient numerical tool is required for predictions of heat transfer behavior and thermally-induced stresses in them. This study presents a finite element formulation of a coupled thermo-mechanical problem in functionally graded metal/ceramic plates. The theoretical framework considers the finite element method (FEM) which is applied to the development of a functionally graded two-dimensional plane strain finite element. The plane strain graded finite element is incorporated within the ABAQUS tm code via the combination of user-defined subroutines. The subroutines enable us to program graded mechanical and thermal properties of the FGM as continuous position-dependent functions and, then, to sample them directly at the Gauss integration points of the element. The performance of the developed graded finite element is verified by comparisons with results known in the literature and with calculated using conventional homogeneous elements in a layered model. The solutions of thermomechanical problems of functionally graded plates referring to pure mechanical and thermal tasks, and uncoupled and coupled analyses of thermoelasticity are carried out and discussed in the paper. Highlights• A finite element formulation of the coupled thermo-mechanical problem of a FGM plate is presented.• A graded plain strain element is incorporated within the ABAQUS code environment.• The performance of the graded element is validated by solving thermo-mechanical problems.• The examples reveal a high accuracy and efficiency of the developed graded finite element. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 *Highlights AbstractFor better understanding of the behavior of functionally graded materials (FGM) in high temperature environment, a reliable and efficient numerical tool is required for predictions of heat transfer behavior and thermally-induced stresses in them. This study presents a finite element formulation of a coupled thermo-mechanical problem in functionally graded metal/ceramic plates. The theoretical framework considers the finite element method (FEM) which is applied to the development of a functionally graded two-dimensional plane strain finite element. The plane strain graded finite element is incorporated within the ABAQUS tm code via the combination of user-defined subroutines. The subroutines enable us to program graded mechanical and thermal properties of the FGM as continuous position-dependent functions and, then, to sample them directly at the Gauss integration points of the element. The performance of the developed graded finite element is verified by comparisons with results known in the literature and with calculated using conventional homogeneous elements in a layered mode...

Computational Techniques for The Evaluation of Inhomogeneity Parameters on Transient Conduction in Functionally Graded Layers

“…Modelling functionally graded layer using finite elements requires assigning continuously varying material properties into the layer. The most conventional way to model graded material inhomogeneity involves the use of conventional homogenous elements in successive layers of the mesh, containing own material properties [30]. Hence, stepwise change in properties along the direction of gradation is satisfied.…”

Material Characterization of PMC/TBC Composite Under High Strain Rates and Elevated Temperatures

“…Ductile damage and shear damage were used. Surface based cohesive behavior was also used to account for delamination on interfaces, [35][36][37][38][39][40][41][42][43]. However, there is a lack of material data, information on mesh density, and calculation time.…”

Influence of the composition gradient on the propagation of heat pulses in functionally graded nanomaterials

“…The classical Fourier law (FL) of heat conduction is usually employed in studying heat transfer in FGMs [9][10][11][12][13]. However, in nanodimensional systems, as well as in several nonequilibrium situations (as for example, in miniaturized systems submitted to high-frequency perturbations which are comparable to the reciprocal of the internal relaxation times), both numerical simulations, and experimental observations point out that the limit of validity of FL is clearly exceeded [4,[14][15][16][17][18][19]; therefore, current frontiers in nanotechnology and materials' science require heat-transport equations which go both beyond FL, and beyond the local-equilibrium theory [15,19,20].…”